It comes amid suggestions that around 180 Conservative MPs are preparing to oppose or abstain, including a significant number of Cabinet members, junior ministers and party enforcers, when the proposals are voted on for the first time on Tuesday.

Edmund Costelloe, who quit as chairman of Somerton and Frome Constituency Conservative Association last month over the policy, told Sky News: "It has been bulldozed through, it wasn't in the manifesto, many, many people would not have voted for candidates had it been known. There is a sense of betrayal."

Geoffrey Vero, chairman of the Conservative association in Surrey Heath where Education Secretary Michael Gove is MP, warned the move "may seriously affect David's opportunity to get re-elected at 2015".

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MPs will vote on the proposals, which will also allow civil partners to convert their partnership to a marriage and enable married people to change their legal gender without having to end their union, for the first time when the Marriage (Same Sex Couples) Bill has its second reading.

Backbenchers have made no secret of their opposition to the move and were left even more angered when the Tory leadership made clear in recent days it would not include marriage tax breaks in next month's budget - something that would have been seen as a concession to disgruntled traditionalists.

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But Mr Cameron views the introduction of same-sex marriage as the "Conservative Party delivering the promise it made". He is giving his MPs a free vote on the Bill, which will avoid a technical rebellion, though the high numbers expected to oppose or abstain from within his party will still prove an embarrassment for the Prime Minister. Strong Liberal Democrat and Labour support means the Bill, however, will comfortably reach its next stage.

Culture minister Ed Vaizey insisted the vote would not tear the Tory party apart, and claimed internal divisions over the issue were "good-natured". "We'll see what happens in the vote on Tuesday, various numbers have been bandied about but what I would say is that it is good-natured division," he told Murnaghan on Sky News. "Is this going to tear the Tory party apart? No, I don't think it will. I think there is a difference of opinion among colleagues but it is a civilised debate."

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